Peridynamic Differential Operator for Numerical Analysis
Autor Erdogan Madenci, Atila Barut, Mehmet Dorduncuen Limba Engleză Hardback – 4 mar 2019
This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson’s and Navier’s equations for direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization.
Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.
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Specificații
ISBN-13: 9783030026462
ISBN-10: 3030026469
Pagini: 296
Ilustrații: XI, 282 p. 163 illus., 137 illus. in color.
Dimensiuni: 160 x 241 x 22 mm
Greutate: 0.56 kg
Ediția:1st ed. 2019
Editura: Springer
Locul publicării:Cham, Switzerland
ISBN-10: 3030026469
Pagini: 296
Ilustrații: XI, 282 p. 163 illus., 137 illus. in color.
Dimensiuni: 160 x 241 x 22 mm
Greutate: 0.56 kg
Ediția:1st ed. 2019
Editura: Springer
Locul publicării:Cham, Switzerland
Cuprins
1 Introduction.- 2 Peridynamic Differential Operator.- 3 Numerical Implementation.- 4 Interpolation, Regression and Smoothing.- 5 Ordinary Differential Equations.- 6 Partial Differential Equations.- 7 Coupled Field Equations.- 8 Integro-Differential Equations.- 9 Weak Form of Peridynamics.- 10 Peridynamic Least Squares Minimization.
Notă biografică
Erdogan Madenci is a Professor in the Aerospace and Mechanical Engineering Department of The University of Arizona, Tucson, Arizona, USA. He received his B.S. degrees on both mechanical and industrial engineering, and his M.S. degree in applied mechanics from Lehigh University, Bethlehem, PA in 1980, 1981, and 1982, respectively. He received his Ph.D. degree in engineering mechanics from UCLA in 1987. Prior to joining the University of Arizona, he worked at Northrop Corporation, Aerospace Corporation, and Fraunhofer Institute. Also, he worked at the KTH Royal Institute of Technology, NASA Langley Research Center, Sandia National Labs and MIT as part of his sabbatical leaves. He is the lead author of four books on Peridynamic Differential Operator for Numerical Analysis, Peridynamic Theory and Its Applications, The Finite Element Method Using ANSYS, and Fatigue Life Prediction of Solder Joints. Recently, he started the Journal of Peridynamics and Nonlocal Modeling as the Co-Editor-in-Chief, and is an Associate Editor of ASME Open Journal of Engineering. He is a Fellow of ASME and an Associate Fellow of AIAA.
Pranesh Roy is an Assistant Professor in the Department of Civil Engineering at the Indian Institute of Technology (Indian School of Mines) (IIT-ISM) Dhanbad. He received his B.E. degree in Civil Engineering from Jadavpur University, Kolkata in 2012. He obtained his M.Tech. degree in Structural Engineering from the Indian Institute of Technology (IIT), Delhi in 2014. He received his Ph.D. degree in Civil Engineering from the Indian Institute of Science (IISc), Bangalore in 2019. He worked as a Postdoctoral Research Associate from 2019 to 2021 in Aerospace and Mechanical Engineering at The University of Arizona, USA. Dr. Roy is an expert in the broad area of theoretical and computational solid mechanics. Particularly, his research focuses on nonclassical continuum theories such as peridynamics, phase field theory, and gauge theory of solids.
Deepak Behera is a Postdoctoral Reseacher in the Department of Aerospace and Mechanical Engineering at the University of Arizona. He received his B.Tech.-M.Tech. dual degree in Aerospace Engineering from the Indian Institute of Technology (IIT), Kanpur in 2012. He received his Ph.D. degree in Aerospace Engineering from the University of Arizona in 2022. Prior to his Ph.D., he worked as a structural engineer at General Electric-Aviation, Bengaluru and IIT, Kanpur. He also worked at Idaho National Lab as a summer visiting scholar. His research focuses on numerical methods and theoretical and computational solid mechanics with an emphasis on failure analysis and peridynamics. His other research interest includes molecular dynamics, optimization, and uncertainty quantification.
Textul de pe ultima copertă
This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities. PD also serves as a natural filter to smooth noisy data and to recover missing data.
This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson’s and Navier’s equationsfor direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization.
Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.
This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson’s and Navier’s equationsfor direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization.
Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.
Caracteristici
Introduces a new computational method to advance the analysis of discrete data and the solutions to field equations of many physical phenomena Provides access to sample algorithms for researchers and student to self-study and discover their own solutions to problems Offers a comprehensive introduction to this emerging method suitable for graduate courses